Abstract
Action potential duration (APD) heterogeneity of cardiac tissue is one of the most important factors underlying initiation of deadly cardiac arrhythmias. In many cases such heterogeneity can be measured at tissue level only, while it originates from differences between the individual cardiac cells. The extent of heterogeneity at tissue and single cell level can differ substantially and in many cases it is important to know the relation between them. Here we study effects from cell coupling on APD heterogeneity in cardiac tissue in numerical simulations using the ionic TP06 model for human cardiac tissue. We show that the effect of cell coupling on APD heterogeneity can be described mathematically using a Gaussian Green's function approach. This relates the problem of electrotonic interactions to a wide range of classical problems in physics, chemistry and biology, for which robust methods exist. We show that, both for determining effects of tissue heterogeneity from cell heterogeneity (forward problem) as well as for determining cell properties from tissue level measurements (inverse problem), this approach is promising. We illustrate the solution of the forward and inverse problem on several examples of 1D and 2D systems.
Highlights
Cardiac contraction is initiated by electrical waves of excitation propagating through cardiac tissue
In this article we show that such electrotonic effects on action potential duration (APD) heterogeneity can be characterized by a linear approach using Gaussian functions fits
After trying several types of sigmoidal functions, we found that an almost perfect fit of spatial APD distribution can be obtained using the error function, which is the antiderivative of the Gaussian function
Summary
Cardiac contraction is initiated by electrical waves of excitation propagating through cardiac tissue. Wave propagation in the heart is a result of succesive excitation of individual cardiac cells, which are electrically coupled to each other by gap junctions. If we use these measured values as APD values at cell level, we can fit the parameters of a cell model to reproduce such APD at a given location. The question how to recover real heterogeneity from tissue level experiments and how heterogeneity at cell level manifests itself at tissue level is very important both for theoretical and experimental work
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